While adding new capabilities, the distributed energy resource proliferation raises great concern about challenges such as dynamic fluctuations of voltages. For example, in a volatile setting with highly uncertain renewable generation and customer consumption, it is challenging to provide reliable power and voltage prediction for operational planning purposes to mitigate risks, e.g., over-voltages. In this paper, we propose an integrated Gaussian Process-based method (IGP) for electric load (consumption minus generation) prediction. For improving the forecasting accuracy, we use not only the data streams generated by the target customer but also those of relevant customers in the feeder system. An adaptive data communication rate controlling scheme is further proposed for dimension reduction of streaming data to address the situation when bandwidth limit enforces a constraint in some feeders. The goal is to make IGP with the same prediction precision but significantly less streaming data amount. The superior efficacy and efficiency of IGP and its enhanced variants are tested and verified on the standard IEEE 8-bus and 123-bus distribution test cases.